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Table 1 Ordered (1) and disordered (2) reaction mechanisms for multistate phosphorylation

From: Multistate Model Builder (MSMB): a flexible editor for compact biochemical models

Reaction Type Rate law
1. XP(i {0:N-1 }) + Kin -> XP(succ(i)) + Kin MA k
2. XP(i {0:N-1 }) + Kin -> XP(succ(i)) + Kin UD dis(N,XP.i,k,XP,Kin)
Function definition Equation
dis(GLQ N, SITE i, GLQ k, SUB X, SUB K) (N-i) * k * X * K
  1. Case 2 depends on the number of unphosphorylated states, so its rate law has to be expressed using a user defined (UD) type (instead of using mass action, MA) with a rate law function, called “dis”. The function definition is also shown. Each formal parameter has a different type (GLQ for global quantity, SITE to refer to the numerical state value of a site of a multistate species, and SUB for the substrate of the current reaction).